ISOTOPES OF POTASSIUM A. KEITH BREWER Bureau of Chemistry and Soils, U. S. Department of Agriculture, Washington, D. C.
P
a t 1 cm. pressure of air operates on sixteen 45-volt B batteries. The background count is very close to 2 per minute which is the limit obtainable due to cosmic rays. The counter can be calibrated by means of a standard made from a known quantity of uranium oxide (U~OS). The salts to be tested are placed directly below the aluminum window. A photograph of the counter and amplification circuit is shown in Figure 2. The impulses received by the anode are amplified by three vacuum tubes; the Johnson and Street circuit (8) is used. The amplified current, in turn, operates a telegraph relay which is connected mechanically to the escapement of a dollar watch, so that each individual ray entering the counter causes the watch to move one-half second. The results obtained in the present experiments (4) confirmed those of other investigations in that only beta and gamma rays were detected (9),the ratio of beta to gamma rays being very close to 100 to 1 ( 2 ) . NUMBER AND ENERGY OF RAYS. A direct count of the rays from a potassium chloride surface morethan 3 mm.in thickness showed that, where the necessary corrections for the geometry of the apparatus were applied, 44 beta rays per minute were emitted in the upward direction for each square centimeter of surface. The energy of the rays was measured by observing the decrease in the number of counts when aluminum foil was placed between the salt and the counter. The decrease in the number of counts as a function of the thickness of aluminum obeys the equation,
OTASSIUM is unique among the elements now considered necessary to sustain life, since it alone is radioactive. This radioactivity makes potassium one of the most interesting of all the elements as far as the past geological history of the earth is concerned. Radioactivity of Potassium NATUREOF RAYS. The Geiger counter is the most convenient method for the detection of radioactivity. It consists simply of an anode and a cathode sealed in a convenient chamber; the gas pressure between the electrodes is usually about I cm. A voltage is applied to the cathode; this voltage is below the breakdown potential of the gas but above the
Glass Tube to Vacuum. System Hard
Wax4
vNickel or Copper Rod, V16" d l a
Hard Rubber Plug
Copper Cylinder W4" d ia,
1, Holes, 3/32"dia/
0.0005"thick
where p t
FIQURE 1. GEIGERCOUNTERFOR BETARAYS
operating potential of the tube for a glow discharge. This voltage is such that the formation of one ion pair in the space between the electrodes will cause a discharge to break from the cathode to the anode. The anode is connected to an amplifying and recording circuit. Under proper conditions the tube will record each individual ray passing between the electrodes. The conventional Geiger counter tubes have a stray or background count of about 20 per minute. Since the radioactivity of potassium is small, it was necessary to design a counter with a low background. Two types of counters have been developed in this laboratory, with background counts as low as 2 per minute; in one case the salt to be tested is placed directly in the counter itself and in the other the rays are admitted through a thin aluminum window. The latter is by far the more satisfactory for the detection of all except extremely soft rays. A schematic drawing of the counter used in this study is shown in Figure 1. The counter
=
=
N = N o e-Pt absorption coefficient thickness
FIQURB 2. COUNTER AND AMPLIFICATION CIRCUIT a93
VOL. 30, NO. 8
INDUSTRIAL AND ENGINEERING CHEMISTRY
894
The value of p so obtained is very close to 30. p for the beta says from potassium has been estimated by other methods (S), an average value near 46 being found; this uncertainty in the value of ,u introduces the only appreciable error in these calculations. The value of ,u = 30 gives 0.55 mm. for the range of the average beta particle in potassium chloride and 2.2 mm. for the maximum range. Expressed in terms of the velocity of light, the maximum velocity is about 0.94~ and the average velocity is 0.85~. ABUNDANCE OF RADIOACTIVE ISOTOPE. In order to determine the disintegration constant and half-life from the measurements given above it is necessary to know which of the potassium isotopes is radioactive and its relative abundance. An estimation of the number and abundance of isotopes necessitates the use of a mass spectrograph. This instrument is described in detail later in the paper. A mass spectrogram for the isotopes of potassium is shown in Figure 5. Potassium has three isotopes of masses 39, 40, and 41, in proportion 8300, 1, and 585, respectively. No other isotopes are present to a t least 1 part in 200,000 (IO). With the number and abundance of the isotopes known, it is possible to determine which isotope is responsible for the radioactivity and to calculate the radioactive constants. Upon the emission of a beta particle an element is transmuted t o the element next higher in atomic number without a change in mass number. There are no known isobars of J P 9 or K41, but 19K4°has two isobars, and KS9 and K4’, therefore, cannot be appreciably radioactive. Smythe and Hemmendinger (11) placed a Geiger counter $directlyin a large mass spectrograph, designed for the quantity separation of isotopes, and observed that the radioactivity was associated with the 40 mass number. It must be concluded, in consequence, that K40 is the radioactive isotope. The disintegration constant for K4O can now be computed by means of the following equation:
.where 92
the flesh to a depth of from 1 to 5 mm. at the rate of ten thousand times per second. Expressed in terms of the threshold of the human senses, the energy liberated from the potassium in one gram of flesh is two hundred times that necessary for the eye to detect if this energy were in the form of green light. Since 19K4° is the radioactive isotope, the disintegration produced for the beta ray emission must be zoCa40. Bramley (3) recently showed the possibility of another type of transmutation which has its basis in the fact that a K4O nucleus may absorb a n extranuclear electron from the K shell to form &A40 with the emission of a gamma ray. The combined disintegration steps, therefore, are:
+
1pK4O+zoCa40 p 1sK4O e +19A40
+
+
Y
The relative rates of production of Ca40 to A4O on the basis of the above mechanisms should be equal to the ratio of beta to gamma rays-namely, 100 to 1. A confirmation of the justification of the application of laboratory experiments to nature is found in the fact that the best available data for the ratio of Ca40 to A40 in the earth’s crust is, within the limits of experimental error, 100 to 1. The formation of argon from potassium is of interest in that it offers a simple explanation for the presence of large amounts of argon deep in the earth’s crust. When the disintegration constant for K40 is known, it is possible to compute the amount of K40 present at any past geological time by the equation :
N/Nt where N Nt
= e-Xt
= present time (taken as unity) = relative increase in number of
K40
time, t , over that extant today
atoms at any past
An upper limit for the age of matter can be obtained from the amount of Ca40 in the earth’s crust. The ratio of Ca40
number of rays emitted per sq. cm. from KC1 60 = minute-second conversion p = absorption coefficient for aluminum (taken as 30) 6 = density of aluminum =
= 9000 is the ratio of K40 to total K. The half-life for K4O computed on the above basis is close to 1.2 billion years. The number of atoms disintegrating per second per gram of potassium is close to 30. The numbeE and energy of the beta rays are illustrated by the following examples. T h e r a y s emitted from the potassium present in the body of a man .weighing 160 p o u n d s will p e n e t r a t e X/K4O
FIGURE 3. DIAGRAM OF MASS SPECTROGR.4PH
UI
C E v o c u o t i o n Channel
M e r c u r y Vapor Pump
- 6.5 cm.
Hq
Vapor Inlet
INDUSTRIAL AND ENGINEERING CHEMISTRY
AUGUST, 1938
to K40 in existence today is 12,400 to 1. The synthesis of this amount of Cad0 will require about 15 billion years a t the present rate of K40 decay. Essentially the same time is required for the production of the existing quantity of Ado from K40 and of Sr*' from Rb*'. For this reason it is reasonable to believe that most, if not all, of the Ca4O and A40 in the earth's crust result from the decomposition of K40. Since this is the case, it follows that the original potassium was quite a different element from that known today. The relative abundance of the present-day potassium isotopes and the most probable abundance for the initial potassium isotopes are as follows: Isotope KSQ K40 K41
Relative Abundance of Isotopes Present Initial 8,300 8,300 1 12,524 585 585
895
mv=HeR
The ions acquire momentum by being accelerated through the potential, E , where Ee
=
l/2mv2
Substituting for v, the dependence of the radius on mass is given by
e = -or 2E m H2R2
R
= k
fi
A photograph of the mass spectrograph in use is shown in Figure 4. A characteristic mass spectrogram for potassium is given in Figure 5. The isotope abundance, as a function of the current received by the collector, is plotted against the mass number, as a function of the magnet current. The
K4O which is now by far the least abundant isotope was originally the most abundant. T t is now interesting to inquire into the possible geological effects that might be expected if it were possible to restore potassium to its original state. From the standpoint of geology it has been shown that the temperature of the earth is maintained about constant a t the present time by the energy liberated from the dissociation of uranium, thorium, and potassium, the three being nearly equal. If the earth behaves as a black body, as seems reasonable, it can be shown that an increase in the energy lost through the earth's surface of about 360 fold will be sufficient to raise the temperature of the earth to the fusion p o i n t n a m e l y , 1000" C. The initial K40 will far more than supply this needed energy (8).
The K39/K4I Ratio The K39/K41isotope ratio has been measured in a wide variety of abundances by means of a mass spectrograph. This particular isotope ratio was chosen for study since it can ratio can be measured with comparative ease; the K3g/K40 be measured only with extreme difficulty. The K39/K41 ratio also has the advantage of enabling the absolute atomic weight to be calculated with a fair degree of accuracy and comparative atomic weights to be studied with a high degree of precision. The mass spectrograph operates on the principle of the familiar left-hand rule for the deflection of an electric current by a magnetic field. A schematic drawing of the mass spectrograph designed for the determination of the abundance ratio of the isotopes of the alkali elements is shown in Figure 3. I n operation, positive ions emitted from the hot platinum disk are accelerated to the filament slit by a potential of several hundred volts. The ion beam is focused on the slit by a suitable potential placed on the focusing shield. The ion beam passing through the filament slit enters the magnetic analyzing chamber where the ions are deflected, the radius of curvature for each ion being a function of its momentum. The ions, that are deflected through 180' with such a curvature that they will emerge from the collector slit, are trapped in a Faraday cage and measured with an FP 54 Pliotron tube. For an ion to be deflected through 180' of arc, the centripetal force acting on the ion must be just balanced by the centrifugal force. Thus, H e R = mvZ/R where H = field strength R = radius of curvature v = velocity of t h e ion
From this it is obvious that, for a given H , the radius is proportional to the momentum,
FIGURE 4. MASSSPECTROGRAPH
abundance ratio is obtained by measuring the height of the isotope peaks. The flat tops of the peaks are due to the fact that the width of the collector slit is greater than that of the resolved ion beams. The mass spectrograph is particularly adaptable for the study of comparative atomic weights since no chemical manipulation is necessary. Only minute amounts of material are needed (a quantity of almost any potassium-containing material no larger than a pinhead is usually sufficient). The measurements can be made in a few hours, and the precision is appreciably greater than can be obtained by ordinary chemical technic. The mass spectrograph illustrated in Figure 4 is designed for measuring isotope abundance ratios. T o compute the atomic weight from the isotope abundance, it is necessary to know the packing fraction for each isotope. The packing fraction is a quantity relating the weight of the isotope to
INDUSTRIAL AND ENGXNEERING CHEMISTRY
896
its mass number. For convenience it is represented by the divergence of the isotope weight from the mass number, divided by the mass number and expressed in parts per 10,000. It represents, therefore, the loss or gain in mass per proton in changing from oxygen to any other element; the proton in 0l6is taken as unity (1). I n computing the atomic weights it is also necessary to know the conversion factor to change from the physical to the chemical scale of weights. The atomic weight computed directly from the isotope abundance is expressed in terms of oxygen isotope 16; the chemical weights refer to ordinary oxygen as 16. Consequently the physical scale is heavier than the chemical by the factor 1.00027. The isotope abundance ratios and the corresponding atomic weights for a wide variety of minerals, and plant and animal tissues have been presented in the literature ( 5 ) . Characteristic results are given in Table I.
2
I \ !
Relotive Abundance K3’= 8300 K4’= I K 4 ’ = 585
/
Sample Minerals: Pacific Ocean water Pacific Ocean water Wyoming shale Wyomingite Hawaiian basalt Puerto Rico clay North Carolina clay Plants: Tobacco Algae Maple Rose leaves Rose leaves Potato vines Potato vines Potato vines Kelp Animals : Muscle tissue Bone marrow Bone marrow Bone marrow Bone marrow Brain Heart Pituitary gland Liver
K33/K4*
14.20 14.20 14.23 14.25 14.11 14.20 14.20
39.0940 39.0940 39,0938 39.0935 39,0947 39.0940 39.0940
....
14.20 14.20 14.20 14.23 13.70 14.GO 14.20 13.77 13.75
39.0940 39.0940 39.0940 39.0938 39.0985 39.0900 39.0940 39.0978 39.0980
Beef Human Horse Bull (old) Veal Rat Auricle Pork Beef
14.21 13.90 13.92 13.80 13.70 14.22 14.28 14.17 14.20
39.0940 39,0967 39,0965 39.0975 39,0985 39.0039
Description Surface
2500 meters
....
Lava Lava Colloidal Red Leaf and stock Fresh water
A B Sprouts Small Mature
39,0933
39.0943 39.0940
The K39/K41 ratio for most substances is near 14.20. The atomic weight computed from this ratio, using the most probable value for the packing fraction, is 39.094 instead of 39.096 which was accepted by the Committee on Atomic Weights. I n comparing atomic weights, therefore, it is necessary to keep in mind the fact that all the weights given are 0.002 lower than the accepted value. Table I shows that the deviation in the abundance ratio for mineral potassium is slight. Plant tissues, in contrast, exhibit appreciable variations in several instances. In general, plant tissues have the abundance ratio of the soil in which they grow but this is not necessarily the case. Kelp with a ratio of 13.75 is grown in water with a ratio of 14.20; the same is true,for nitella and certain other seaweeds. Rose leaves, in contrast, have the abundance ratio of the soil in which they are grown; this is illustrated by leaves A and B where rose A is grown in eastern clay and B is grown in a kelp-fertilized soil. An age effect on the isotope ratio has been noted for potato vines. Although kelp will assimilate about 6 per cent more K41than W9, it will take up about seventy-five times as much potassium as sodium. Animal tissues often exhibit a marked selectivity in their assimilation of potassium isotopes. Bone marrow is conspicuous for its high K41 content; this is interesting since Hoffmann (7) showed that the potassium content of bone marrow is associated with growth. Heart muscle, in contrast, is low in K41.
I I1 -
2-
TABLE I. ISOTOPE ABUNDANCE RATIOS ASD ATOMIC WEIGHTS Computed Atomic Weight
VOL. 30, NO. 8
Mass Number
FIGURE 5.
MASSSPECTROGRAM FOR
POTASSIUM
THE
ISOTOPES OF
Various suggestions have been offered to account for the mechanism by which plant and animal tissues can selectively concentrate certain isotopes. These suggestions usually involve selective adsorption in the cell walls or some form of base exchange. Apparently either mechanism is capable of explaining the observed facts, since comparable separations have been obtained by both methods. While isotope studies of the type discussed in this paper may add to our knowledge of the metabolism of potassium, their principal importance is to indicate the desirability for an investigation of the effect of pure or a t least highly concentrated isotopes on vital processes. I n consequence the prime need is for the development of methods by which the various isotopes can be separated or concentrated. Some success has been attained to date. It is safe to predict that within the next few years concentrates of the isotopes of potassium will be available for biological research and that the results to be found will be of immense interest and importance.
Literature Cited (1) Aston, F. W., “Mass Spectra and Isotopes,” London, Edward Arnold and Co., 1933. (2) Boccisrilli, D., Atti accad. Lincei, 17, 830 (1933). (3) Bramley, A , , Science, 86, 424 (1937). (4) Bramley, A., and Brewer, A. K., Phys. Rev., 53, 502 (1938). (5) Brewer, A. K., J. Am. Chem. Soc., 58, 365, 370 (1936); 59, 869 (1937); Brewer, A. K., and Baudisch, Oskar, Ibid., 59, 1578 (1937). (6) Brewer, A. K., Science, 86, 198 (1937). (7) Hoffmann, T., Biochem. Z . , 243, 145 (1931). (8) Johnson and Street, J. Franklin Inst., 215, 293 (1933). (9) Klemperer, O., Proc. Roll. SOC.(London),A148, 638 (1935). 10) Nier, A. O., Phys. Rev., 48, 283 (1935); Brewer, A. K., Ibid., 48, 640 (1935). 11) Smythe and Hemmendinger, Ibid., 51, 178 (1937). RECEIVEDJune 28, 1938.
The paper ’entitled “Equilibria in the System Potassium Sulfate-Magnesium Sulfate-Calcium Sulfate-Water a t 100” C.,”by J. E. Conley, A. Gabriel, and E. P. Partridge, which wag also presented as part of the Potash Symposium, waa published in the May issue of the Journal of Physical Chemistry [42,587-0163 (193811.
